Timed event system
(Learn how and when to remove this message) The General System has been described in [Zeigler76] and [ZPK00] with the standpoints to define (1) the time base, (2) the admissible input segments, (3) the system states, (4) the state trajectory with an admissible input segment, (5) the output for a given state.
A Timed Event System defining the state trajectory associated with the current and event segments came from the class of General System to allows non-deterministic behaviors in it [Hwang2012]. Since the behaviors of DEVS can be described by Timed Event System, DEVS and RTDEVS is a sub-class or an equivalent class of Timed Event System.
Timed Event Systems
A timed event system is a structure
![{\displaystyle {\mathcal {G}}=<Z,Q,Q_{0},Q_{A},\Delta >}](https://wikimedia.org/api/rest_v1/media/math/render/svg/3553571783de924a617a0f08847c324314eda9c6)
where
is the set of events;
is the set of states;
is the set of initial states;
is the set of accepting states;
is the set of state trajectories in which
indicates that a state
can change into
along with an event segment
. If two state trajectories
and
are called contiguous if
, and two event trajectories
and
are contiguous. Two contiguous state trajectories
and
implies
.
Behaviors and Languages of Timed Event System
Given a timed event system
, the set of its behaviors is called its language depending on the observation time length. Let
be the observation time length. If
,
-length observation language of
is denoted by
, and defined as
We call an event segment
a
-length behavior of
, if
.
By sending the observation time length
to infinity, we define infinite length observation language of
is denoted by
, and defined as
We call an event segment
an infinite-length behavior of
, if
.
See also
State Transition System
References
- [Zeigler76] Bernard Zeigler (1976). Theory of Modeling and Simulation (first ed.). Wiley Interscience, New York.
- [ZKP00] Bernard Zeigler; Tag Gon Kim; Herbert Praehofer (2000). Theory of Modeling and Simulation (second ed.). Academic Press, New York. ISBN 978-0-12-778455-7.
- [Hwang2012] Moon H. Hwang. "Qualitative Verification of Finite and Real-Time DEVS Networks". Proceedings of 2012 TMS/DEVS. Orlando, FL, USA. pp. 43:1–43:8. ISBN 978-1-61839-786-7.